Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

Odds ratio

ORdASPIRIN¼ 1 vs:ASPIRIN¼ 0 ¼expð 1 : 3302 Þ

¼ 0 : 264

Wald test

H 0 :b 1 ¼ 0

Z¼

 1 : 3302

0 : 1444

¼ 9 : 21 ;P¼ 0 : 0001

Score test

H 0 :b 1 ¼ 0
Chi-square¼65.84,P¼0.0001

Note:
Z^2 ¼(9.21)^2 ¼84.82,
so Wald 6 ¼Score

Exchangeable working correlation
matrix
COL1 COL2 ... COL6

ROW1 1.0000 0.0954 ... 0.0954
ROW2 0.0954 1.0000 ... 0.0954
ROW3 0.0954 0.0954 ... 0.0954
ROW4 0.0954 0.0954 ... 0.0954
ROW5 0.0954 0.0954 ... 0.0954
ROW6 0.0954 0.0954 ... 1.0000

^r¼ 0 : 0954

Model 3:SLR (naive model)

Variable Coefficient

Model-based

Std Err

Wald

p-value

INTERCEPT 0.3741 2.0300 0.8538
ASPIRIN 1.3410 0.1676 0.0001
AGE 0.0090 0.0109 0.4108
GENDER 0.5194 0.3036 0.0871
WEIGHT 0.0013 0.0088 0.8819
HEIGHT 0.0078 0.0133 0.5580
SCALE 1.0000 0.0000

The odds ratio for aspirin use is estimated at

exp(1.3302)¼0.264, which suggests that

aspirin is a preventive factor toward throm-

botic graft occlusion after coronary bypass

grafting.

The Wald test can be used for testing the

hypothesisH 0 :b 1 ¼0. The value of theztest

statistic is9.21. TheP-value of 0.0001 indi-

cates that the coefficient for ASPIRIN is statis-

tically significant.

Alternatively, the Score test can be used to test

the hypothesisH 0 :b 1 ¼0. The value of the chi-

square test statistic is 65.34 yielding a similar

statistically significantP-value of 0.0001.

Note, however, that thew^2 version of the Wald

text (i.e., Z^2 ) differs from the Score statistic.

The correlation parameter estimate obtained

from the working correlation matrix is

0.0954, which suggests a negative association

between reocclusion of different arteries from

the same bypass patient compared with reoc-

clusions from different patients.

The output for a standard logistic regression

(SLR) is presented on the left for comparison

with the corresponding GEE models. The

parameter estimates for the standard logistic

regression are similar to those obtained from

the GEE model, although their standard errors

are slightly larger.

554 15. GEE Examples